The solo student pilot reported that during the first landing touchdown, the airplane porpoised, and she elected to abort the landing. She reported that during the second landing touchdown at a different airport, the airplane "started to bounce very hard." A postflight inspection revealed substantial damage to the firewall and to the floor panels underneath the rudder pedals.
The student pilot reported no pre-impact mechanical failures or malfunctions with the airframe or engine that would have precluded normal operation.